Question

cho mn hỏi 

so sánh \(\frac{19^{19}-5}{19^{20}+4}vs\frac{19^{20}-5}{19^{21}+4}\)

Answer 1

Đặt  \(A=\frac{19^{19}-5}{19^{20}+4}\)

\(\Rightarrow19A=\frac{19^{20}-95}{19^{20}+4}=\frac{19^{20}+4-99}{19^{20}+4}=1-\frac{99}{19^{20}+4}\)

\(B=\frac{19^{20}-5}{19^{21}+4}\)

\(\Rightarrow19B=1-\frac{99}{19^{21}+4}\) ( chỗ này bn lm giống như mk ở trên nha! )

\(\Rightarrow\frac{99}{19^{20}+4}>\frac{99}{19^{21}+4}\)

\(\Rightarrow1-\frac{99}{19^{20}+4}< 1-\frac{99}{19^{21}+4}\)

\(\Rightarrow19A< 19B\)

=> A < B